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Proof step 161 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), dent = negdentry((q0 + str0 ').last), err1 = ESUCCESS, inode = getinode(mkdentry(str, entries0[str]).ino, dirs, files), mkdentry(str, entries0[str]).dentry?, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ∧ ispath(q0, ROOT_INO, ino2, dirs, files) ∧ px-parent(user, q0, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(q0, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q0 ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files), links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_may_create#(ino2, dent, user, dirs, files, asynced; inode, err1); new_inode := inode, new_dent := dent; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), q0 + str0 ' = ε, root[q + str '].dir?, entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 162:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 163:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 164:
root[q0].dir? ↔ ino2 ∈ dirs, dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), err1 = ESUCCESS, inode = mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_may_create#(ino2, negdentry((q0 + str0 ').last), user, dirs, files, asynced; inode, err1); new_inode := inode, new_dent := negdentry((q0 + str0 ').last); if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)% ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ESUCCESS ≠ ENOENT; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ mkdentry(str, m).dentry?; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m).ino = m; (s)